Can router be ilnfected? Does reset to factory clear all?

I have been having a problem for about the last week with my internet service getting so slow it won't even pull up a page when this happens. The computers will show that I am connected to one of my routers and it will indicate internet access but I am not able to pull anything up. Even Iphone will be connected but won't go to page either. Like it times out. Here is the setup that I have. This is in my home. I have a cable modem that is supplied by TimeWarnerCablel. It has the coax cable that feeds it, from there I have an ethernet cable that runs from modem to first router which is a Netgear N router. From that router I have an ethernet cable that goes from router 1 to another router, I will call this router #2, it is also a Netgear N router, then there is an ethernet cable that runs out of router 2 and plugs into a desktop computer. When this happens I disconnect the routers from the modem and do a reset on the modem. I have 3 laptops that use the wifi and we use a ROKU to stream tv.